Harden, SJ; (2013) Weighted composite likelihoods. Doctoral thesis , UCL (University College London).

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Abstract

For analysing complex multivariate data, the use of composite surrogates is a well established tool. Composite surrogates involve the creation of a surrogate likelihood that is the product of low dimensional margins of a complex model, and result in acceptable parameter estimators that are relatively inexpensive to calculate. Some work has taken place in adjusting these composite surrogates to restore desirable features of the data generating mechanism, but the adjustments are not specific to the composite world: they could be applied to any surrogate. An issue that has received less attention is the determination of weights to be attached to each marginal component of a composite surrogate. This issue is the main focus of this thesis. We propose a weighting scheme derived analytically from minimising the Kullback-Leibler Divergence (KLD) between the data generating mechanism and the composite surrogate, treating the latter as a bona fide density which requires consideration of a normalising constant (a feature which is usually ignored). We demonstrate the effect of these weights for a simulation. We also derive an explicit formulation for the weights when the composite components are multivariate normal and, in certain cases, show how they can be used to restore the original data generating mechanism.

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